{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. Kernel Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from prml.kernel import (\n",
    "    PolynomialKernel,\n",
    "    RBF,\n",
    "    GaussianProcessClassifier,\n",
    "    GaussianProcessRegressor\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_toy_data(func, n=10, std=1., domain=[0., 1.]):\n",
    "    x = np.linspace(domain[0], domain[1], n)\n",
    "    t = func(x) + np.random.normal(scale=std, size=n)\n",
    "    return x, t\n",
    "\n",
    "def sinusoidal(x):\n",
    "        return np.sin(2 * np.pi * x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.1 Dual Representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=10, std=0.1)\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "model = GaussianProcessRegressor(kernel=PolynomialKernel(3, 1.), beta=int(1e10))\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "y = model.predict(x)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4 Gaussian Processes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4.2 Gaussian processes for regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=7, std=0.1, domain=[0., 0.7])\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 15.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr\")\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4.3 Learning the hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=7, std=0.1, domain=[0., 0.7])\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 1.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr {}\".format(model.kernel.params))\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "model.fit(x_train, y_train, iter_max=100)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr {}\".format(np.round(model.kernel.params, 2)))\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4.4 Automatic relevance determination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_toy_data_3d(func, n=10, std=1.):\n",
    "    x0 = np.linspace(0, 1, n)\n",
    "    x1 = x0 + np.random.normal(scale=std, size=n)\n",
    "    x2 = np.random.normal(scale=std, size=n)\n",
    "    t = func(x0) + np.random.normal(scale=std, size=n)\n",
    "    return np.vstack((x0, x1, x2)).T, t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data_3d(sinusoidal, n=20, std=0.1)\n",
    "x0 = np.linspace(0, 1, 100)\n",
    "x1 = x0 + np.random.normal(scale=0.1, size=100)\n",
    "x2 = np.random.normal(scale=0.1, size=100)\n",
    "x = np.vstack((x0, x1, x2)).T\n",
    "\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 1., 1., 1.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(x_train[:, 0], y_train, facecolor=\"none\", edgecolor=\"b\", label=\"training\")\n",
    "plt.plot(x[:, 0], sinusoidal(x[:, 0]), color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.plot(x[:, 0], y, color=\"r\", label=\"gpr {}\".format(model.kernel.params))\n",
    "plt.fill_between(x[:, 0], y - y_std, y + y_std, color=\"pink\", alpha=0.5, label=\"gpr std.\")\n",
    "plt.legend()\n",
    "plt.ylim(-1.5, 1.5)\n",
    "\n",
    "model.fit(x_train, y_train, iter_max=100, learning_rate=0.001)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x_train[:, 0], y_train, facecolor=\"none\", edgecolor=\"b\", label=\"training\")\n",
    "plt.plot(x[:, 0], sinusoidal(x[:, 0]), color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.plot(x[:, 0], y, color=\"r\", label=\"gpr {}\".format(np.round(model.kernel.params, 2)))\n",
    "plt.fill_between(x[:, 0], y - y_std, y + y_std, color=\"pink\", alpha=0.2, label=\"gpr std.\")\n",
    "plt.legend()\n",
    "plt.ylim(-1.5, 1.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 6.4.5 Gaussian processes for classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def create_toy_data():\n",
    "    x0 = np.random.normal(size=50).reshape(-1, 2)\n",
    "    x1 = np.random.normal(size=50).reshape(-1, 2) + 2.\n",
    "    return np.concatenate([x0, x1]), np.concatenate([np.zeros(25), np.ones(25)]).astype(np.int)[:, None]\n",
    "\n",
    "x_train, y_train = create_toy_data()\n",
    "x0, x1 = np.meshgrid(np.linspace(-4, 6, 100), np.linspace(-4, 6, 100))\n",
    "x = np.array([x0, x1]).reshape(2, -1).T\n",
    "\n",
    "model = GaussianProcessClassifier(RBF(np.array([1., 7., 7.])))\n",
    "model.fit(x_train, y_train)\n",
    "y = model.predict(x)\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train.ravel())\n",
    "plt.contourf(x0, x1, y.reshape(100, 100), levels=np.linspace(0,1,3), alpha=0.2)\n",
    "plt.colorbar()\n",
    "plt.xlim(-4, 6)\n",
    "plt.ylim(-4, 6)\n",
    "plt.gca().set_aspect('equal', adjustable='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
